Embed Size (px)
Citation preview
Tools and Algorithms for Querying and Mining Large Graphs
Hanghang TongMachine Learning Department
Carnegie Mellon [email protected]
http://www.cs.cmu.edu/~htong
1
Thesis Committee
• Christos Faloutsos• William Cohen• Jeff Schneider• Philip S. Yu
2
Graphs are everywhere!
3
Motivating Questions: (high level)• Given a large graph, we want to
4
R. Agrawal Jiawei Han
V. Vapnik M. Jordan
H.V. Jagadish
Laks V.S. Lakshmanan
Heikki Mannila
Christos Faloutsos
Padhraic Smyth
Corinna Cortes
15 1013
1 1
6
1 1
4 Daryl Pregibon
10
2
11
3
16
CePS on DBLP [Tong+ KDD 06] T3 on CIKM [Tong+ CIKM 08]
+Task A: Querying +Task B: Mining
Will return to this later…
Motivating Questions (in details)
• Querying [Goal: query complex relationship]– Q.1. Find complex user-specific patterns;– Q.2. Link Prediction & Proximity Tracking;– Q.3. Answer all the above questions quickly.
• Mining [Goal: find interesting patterns]– M.1. Spot Anomalies; – M.2. Mine time & space;– M.3. Detect communities.
5
Thesis Overview
6
Q1
Q3
Q2Q2
Q3
M1
M2
M3M3
M1
M2
Thesis Overview
7
CePS, G-Ray, ProSIN (KDD06, KDD07 a, ICDM08)Q1
FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3
pTrack/cTrack (SDM08, SAM08)Q2
DAP(KDD07 b)
Q2
FastProx(SDM08, SAM08)Q3P3
Colibri-D(KDD08 b)
M1
T3/MT3 (CIKM08)
M2
P1M3P1M3
Colibri-S(KDD08 b)M1 P3
P3
Completed Proposed
Questions That We Ask
P2M2 P3
Tasks Impact, ApplicationsQ1 Identify master-mind criminal; money launder ring;
interactive search & summarization
Q2 Predict who-calls-whom; Trend analysis on graph level
Q3 Scale all the above app.s to large, disk resident, graphs
M1 Efficient anomaly detection in an intuitive, dynamic way
M2 Mine time/space in complex settings
M3 Detect community w/ optional constraints
Thesis Overview: Impact
Qu
erying
Min
ing
8
Footnote: Our work for Q1 has been transferred into IBM product (Cyano)
Roadmap• Introduction• Completed Work
–Querying–Mining
• Proposed Work
9
• Preliminary
• Q1
• Q2
• Q3
Preliminary: Proximity Measurement
10
A BH1 1
D1 1
E
F
G1 11
I J1
1 1
a.k.a Relevance, Closeness, ‘Similarity’…
Thesis Overview
11
CePS, G-Ray, ProSIN (KDD06, KDD07 a, ICDM08)Q1
FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3
pTrack/cTrack (SDM08, SAM08)Q2
DAP(KDD07 b)Q2
FastProx(SDM08, SAM08)Q3P3
Colibri-D(KDD08 b)
M1
T3/MT3 (CIKM08)
M2
P1M3P1M3
Colibri-S(KDD08 b)M1 P3
P3
Completed Proposed
Questions That We Ask
P2M2 P3
Competed work on Q1
• Goal: Find complex user-specific patterns, – Q1.1. Center-Piece Subgraph Discovery,
– e.g., master-mind criminal given some suspects X, Y and Z?
– Q1.2. Best Effort Pattern Match, – e.g., Money-laundry ring
– Q1.3 Interactive querying (e.g. Negation)– e.g., find most similar conferences wrt KDD, but not like
ICML?
12
Q1.1 Center-Piece Subgraph Discovery [Tong+ KDD 06]
A C
B
A C
B
Original GraphCePS
Q: How to find hub for the black nodes?
CePS Node
Input Output
Red: Max (Prox(A, Red) x Prox(B, Red) x Prox(C, Red))
CePS: Example (AND Query)
R. Agrawal Jiawei Han
V. Vapnik M. Jordan
H.V. Jagadish
Laks V.S. Lakshmanan
Heikki Mannila
Christos Faloutsos
Padhraic Smyth
Corinna Cortes
15 1013
1 1
6
1 1
4 Daryl Pregibon
10
2
11
3
16
14
DBLP co-authorship network: - 400,000 authors, 2,000,000 edges
K_SoftAND: Relaxation of AND
Asking AND query? No Answer!
Disconnected Communities
Noise
15
R. Agrawal Jiawei Han
V. Vapnik M. Jordan
H.V. Jagadish
Laks V.S. Lakshmanan
Umeshwar Dayal
Bernhard Scholkopf
Peter L. Bartlett
Alex J. Smola
1510
13
3 3
5 2 2
327
4
CePS: 2 SoftAND
Stat.
DB
16
Output
Data Graph
Query Graph
Matching SubgraphAccountant
CEO
Manager
SEC
Q: How to find matching subgraph?
Q1.2. Best-Effort Pattern Match [Tong+ KDD 2007 b]
Input
Interception
G-Ray: How to?
matching node
matching node
matching node
matching node
Goodness = Prox (12, 4) x Prox (4, 12) x Prox (7, 4) x Prox (4, 7) x Prox (11, 7) x Prox (7, 11) x Prox (12, 11) x Prox (11, 12)
details
Observation: , etc. 18
Effectiveness: star-query
Query Result
Databases
Bio-medicalIntelligent Agent
19
Effectiveness: line-query
Query
Result
Databases Learning Bio-medicalTheory
20
Q1.3: Interactive Querying
21
User Feedback
User Feedback
User Feedback
User Feedback
Initial Results No to `ICML’ Yes to `SIGIR’
'ICDM' 'ICML' 'SDM' 'VLDB' 'ICDE'
'SIGMOD' 'NIPS''PKDD''IJCAI'
'PAKDD'
'ICDM' 'SDM''PKDD''ICDE''VLDB'
'SIGMOD''PAKDD''CIKM''SIGIR'
'WWW'
'SIGIR''TREC''CIKM''ECIR''CLEF''ICDM''JCDL''VLDB''ACL''ICDE'
two main sub-communities in KDD: DBs (green) vs. Stat (Red)
Negative feedback on ICML will exclude other stats confs (NIPS, IJCAI)
Positive feedback on SIGIR will bring more IR (brown) conferences.
what are most related conferences wrt KDD?(DBLP author-conference bipartite graph) 22
Q1.3 ProSIN for Interactive Querying
[Tong+ ICDM 08]
Q1.3 ProSIN for Interactive Querying
[Tong+ ICDM 08]Initial Results No to `ICML’ Yes to `SIGIR’
'ICDM' 'ICML' 'SDM' 'VLDB' 'ICDE'
'SIGMOD' 'NIPS''PKDD''IJCAI'
'PAKDD'
'ICDM' 'SDM''PKDD''ICDE''VLDB'
'SIGMOD''PAKDD''CIKM''SIGIR'
'WWW'
'SIGIR''TREC''CIKM''ECIR''CLEF''ICDM''JCDL''VLDB''ACL''ICDE'
two main sub-communities in KDD: DBs (green) vs. Stat (Red)
Negative feedback on ICML will exclude other stats confs (NIPS, IJCAI)
Positive feedback on SIGIR will bring more IR (brown) conferences.
what are most related conferences wrt KDD?(DBLP author-conference bipartite graph) 23
Initial Results No to `ICML’ Yes to `SIGIR’
'ICDM' 'ICML' 'SDM' 'VLDB' 'ICDE'
'SIGMOD' 'NIPS''PKDD''IJCAI'
'PAKDD'
'ICDM' 'SDM''PKDD''ICDE''VLDB'
'SIGMOD''PAKDD''CIKM''SIGIR'
'WWW'
'SIGIR''TREC''CIKM''ECIR''CLEF''ICDM''JCDL''VLDB''ACL''ICDE'
two main sub-communities in KDD: DBs (green) vs. Stat (Red)
Negative feedback on ICML will exclude other stats confs (NIPS, IJCAI)
Positive feedback on SIGIR will bring more IR (brown) conferences.
what are most related conferences wrt KDD?(DBLP author-conference bipartite graph) 24
Q1.3 ProSIN for Interactive Querying
[Tong+ ICDM 08]
Thesis Overview
25
CePS, G-Ray, ProSIN (KDD06, KDD07 a, ICDM08)Q1
FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3
pTrack/cTrack (SDM08, SAM08)Q2
DAP(KDD07 b)Q2
FastProx(SDM08, SAM08)Q3P3
Colibri-D(KDD08 b)
M1
T3/MT3 (CIKM08)
M2
P1M3P1M3
Colibri-S(KDD08 b)M1 P3
P3
Completed Proposed
Questions That We Ask
P2M2 P3
Q2.1 Link Prediction: direction [Tong+ KDD 07 a]
• Q: Given the existence of the link,
what is the direction of the link?
• A: (DAP) Compare Prox(ij) and Prox(ji)>70%
Prox (ij) - Prox (ji)
density
i
j
i
i
i
26
?
Web Link - 4, 000 nodes - 10, 000 edges
Q2.2 pTrack/cTrack: Challenge[Tong+ SDM 08]
• Observations (CePS, GRay, ProSIN…)– All for static graphs– Proximity: main tool
• Graphs are evolving over time!– New nodes/edges show up; – Existing nodes/edges die out; – Edge weights change…
Q: How to make everything incremental? A: Track Proximity! 27
pTrack/cTrack: Trend analysis on graph level
M. Jordan
G.HintonC. Koch
T. Sejnowski
Year
Rank of Influence
28
pTrack: Problem Definitions
• [Given] – (1) a large, skewed time-evolving bipartite graphs, – (2) the query nodes of interest
• [Track] – (1) top-k most related nodes for each query node
at each time step t; – (2) the proximity score (or rank of proximity)
between any two query nodes at each time step t
29
pTrack: Philip S. Yu’s Top-5 conferences up to each year
ICDE
ICDCS
SIGMETRICS
PDIS
VLDB
CIKM
ICDCS
ICDE
SIGMETRICS
ICMCS
KDD
SIGMOD
ICDM
CIKM
ICDCS
ICDM
KDD
ICDE
SDM
VLDB
1992 1997 2002 2007
DatabasesPerformanceDistributed Sys.
DatabasesData Mining
DBLP: (Au. x Conf.) - 400k aus, - 3.5k confs - 20 yrs
30
KDD’s Rank wrt. VLDB over yearsProx. Rank
Year
Data Mining and Databases are getting closer & closer
31
(Closer)
cTrack:10 most influential authors in NIPS community up to each year
Author-paper bipartite graph from NIPS 1987-1999. 1740 papers, 2037 authors, spreading over 13 years
T. Sejnowski
M. Jordan
32
Thesis Overview
33
CePS, G-Ray, ProSIN (KDD06, KDD07 a, ICDM08)Q1
FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3
pTrack/cTrack (SDM08, SAM08)Q2
DAP(KDD07 b)Q2
FastProx(SDM08, SAM08)Q3P3
Colibri-D(KDD08 b)
M1
T3/MT3 (CIKM08)
M2
P1M3P1M3
Colibri-S(KDD08 b)M1 P3
P3
Completed Proposed
Questions That We Ask
P2M2 P3
Proximity is the main tool• Q.1: CePS, G-Ray, ProSIN• Q.2: DAP, pTrack/cTrack
34
Q: What is a `good’ Score?
A BH1 1
D1 1
E
F
G1 11
I J1
1 1
a.k.a Relevance, Closeness, ‘Similarity’…
Random walk with restart [Pan+ KDD 2004]
Node 4
Node 1Node 2Node 3Node 4Node 5Node 6Node 7Node 8Node 9Node 10Node 11Node 12
0.130.100.130.220.130.050.050.080.040.030.040.02
1
4
3
2
56
7
910
811
120.13
0.10
0.13
0.13
0.05
0.05
0.08
0.04
0.02
0.04
0.03
Ranking vector More red, more relevant
Nearby nodes, higher scores
4r
2c 3cQ c ...W 2W 3W
Why RWR is a good score?
all paths from i to j with length 1
all paths from i to j with length 2
all paths from i to j with length 3
W : adjacency matrix. c: damping factor
1( )Q I cW ,( , ) i jQ i j r
i
j
RWR summarizes all the weighted paths from i to j
Computing RWR• OntheFly
– No Pre-Computation; – Light Storage Cost (W)– Slow On-Line Response: O(mE)
• Pre-Compute– Fast On-Line Response – Prohibitive Pre-Compute Cost: O(n3)– Prohibitive Storage Cost: O(n2)
37
~
1( )Q I cW
[ 1] [ ] (1 )i i ir t cWr t c e
Q: How to Balance?
On-line Off-line
38
Goal: Efficiently Get (elements) of 1( )Q I cW
B_Lin: Basic Idea[Tong+ ICDM 2006]
1
43
2
5 6
7
9 10
811
120.130.10
0.13
0.13
0.05
0.05
0.08
0.04
0.02
0.04
0.03
1
4
3
2
56
7
910
811
12
Find Community
Fix the remaining
Combine1
43
2
5 6
7
9 10
811
12
1
43
2
5 6
7
9 10
811
12
56
7
910
811
12
1
43
2
5 6
7
9 10
811
12
1
4
3
2
5 6
7
910
811
12
1
4
3
2
39
+~~
B_Lin: details
Cross community
details
40
+=
B_Lin: details
W~I – c ~~ I – c – cUSVW1~
-1 -1
Easy to be inverted LRA difference
Sherman–Morrison Lemma!
details
41If Then
B_Lin: summary
• Pre-Compute Stage• Q: • A: A few small, instead of ONE BIG, matrices inversions
• On-Line Stage• Q: Efficiently recover one column of Q• A: A few, instead of MANY, matrix-vector multiplications
Efficiently compute and store Q
42
Query Time vs. Pre-Compute Time
Log Query Time
Log Pre-compute Time
•Quality: 90%+ •On-line:
•Up to 150x speedup•Pre-computation:
•Two orders saving
43
Our Results
More on Scalability Issues for Querying(the spectrum of ``FastProx’’)
• B_Lin: one large linear system – [Tong+ ICDM06, KAIS08]
• BB_Lin: the intrinsic complexity is small – [Tong+ KAIS08]
• FastUpdate: time-evolving linear system – [Tong+ SDM08, SAM08]
• FastAllDAP: multiple linear systems – [Tong+ KDD07 a]
• Fast-ProSIN: dealing w/ on-line feedback– [Tong+ ICDM 2008]
44
Roadmap• Introduction• Completed Work
–Querying–Mining
• Proposed Work
45
• M1: Spotting Anomalies
• M2: Mining Time
Thesis Overview
46
CePS, G-Ray, ProSIN (KDD06, KDD07 a, ICDM08)Q1
FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3
pTrack/cTrack (SDM08, SAM08)Q2
DAP(KDD07 b)Q2
FastProx(SDM08, SAM08)Q3P3
Colibri-D(KDD08 b)
M1
T3/MT3 (CIKM08)
M2
P1M3P1M3
Colibri-S(KDD08 b)M1 P3
P3
Completed Proposed
Questions That We Ask
P2M2 P3
Motivation [Tong+ KDD 08 b]
• Q: How to find patterns?– e.g., communities, anomalies, etc.
• A: Low-Rank Approximation (LRA) for Adjacency Matrix of the Graph.
A L
M RX X
~~47
LRA for Graph Mining: Example
John
KDD
Tom
Bob
Carl
Van
RoyRECOMB
ISMB
ICDM
Author Conf.
L M R
~~X X
Adj. matrix: A
Au. clusters
Conf. Cluster
Interaction
Recon. error is high ‘Carl’ is abnormal
48
Challenges: How to get (L, M, R)?
• Efficiently • both time and space
• Intuitively• easy for interpretation
• Dynamically • track patterns over time
49
None of Existing Methods Fully Meets Our Wish List!
Why Not SVD and CUR/CX?
• SVD: Optimal in L2 and LF
– Efficiency• Time:• Space: (L, R) are dense
– Interpretation• Linear Combination of
many columns
– Dynamic: Not Easy
50
2 2(min( , ))O n m nm
• CUR: Example-based– Efficiency
• Better than SVD• Redundancy in L
– Interpretation• Actual Columns from A
xxxx
– Dynamic: Not Easy
Solutions: Colibri [Tong+ KDD 08 b]
• Colibri-S: for static graph– Basic idea: remove linear redundancy– Same accuracy as CUR/CX– Significant savings in both time & space
• Up to 53x speed-up
• Colibri-D: for dynamic graph– Basic idea: leverage smoothness between time – Same accuracy as CUR/CMD
• Up to 112x speed-up
51
details
A Pictorial Comparison (for static graphs)
52
1st singular vector
2nd singular vector
SVD CUR
CMD Colibri-S
details
Comparison SVD, CUR vs. Colibri
s
Wish List SVD [Golub+ 1989]
CUR/CX[Drineas+ 2005]
Colibri[Tong+ 2008]
Efficiency
Interpretation
Dynamics53
details
Performance of Colibri-S
Time Space
Ours
CUR CUR
CMD
OursCMD
• Accuracy• Same 91%+
• Time• 12x of CMD• 28x of CUR
• Space• ~1/3 of CMD• ~10% of CUR
54Data set: Network traffic
- 21,837 sources/destinations, 158,805 edges
Performance of Colibri-D
Time
# of changed cols
CMD
Colibri-S
Colibri-D achieves up to 112x speedups
Colibri-D
55
Network traffic
- 21,837 nodes
- 1,220 hours
- 22,800 edge/hr
Thesis Overview
56
CePS, G-Ray, ProSIN (KDD06, KDD07 a, ICDM08)Q1
FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3
pTrack/cTrack (SDM08, SAM08)Q2
DAP(KDD07 b)Q2
FastProx(SDM08, SAM08)Q3P3
Colibri-D(KDD08 b)
M1
T3/MT3 (CIKM08)
M2
P1M3P1M3
Colibri-S(KDD08 b)M1 P3
P3
Completed Proposed
Questions That We Ask
P2M2 P3
M2: How to mine time in some complex context?
[Tong+ CIKM 08]
57
A Motivating Example: InputsTime Event(e.g., Session) EntityOct. 26 Link Analysis Tom, Bob
Clustering Bob, AlanOct. 27 Classification Bob, Alan
Anomaly Detection Alan, BeckOct. 28 Party Beck, DanOct. 29 Web Search Dan, Jack
Advertising Jack, PeterOct. 30 Enterprise Search Jack, PeterOct. 31 Q & A Peter, Smith
58
Time Cluster, rep. entities: b7,b6, b8A Motivating Example: Outputs
JackOct. 29
Oct. 30Oct. 30
Oct. 28
Oct. 26
Oct. 27
Time Cluster Rep. Entities:
``Jack’’, ``Peter’’, ``Smith’’
Abnormal Time Rep. Entities:
``Beck’’ , ``Dan’’
Time Cluster Rep. Entities:
``Tom’’, ``Bob’’, ``Alan’’
Problem Definitions (How to mine time in such complex context)
• Given data sets collected at different time stamps;
• We want to find +1: Time Clusters+2: Abnormal Time stamps+3: Interpretations+4: Right time granularity
60
T3
MT3
Our Solutions
Data Sets• CIKM: from CIKM proceedings
• Time: Publication year (1993-2007, 15)• Event: Paper-published (952)• Entities: Author (1895) & Session (279)• Attribute: Keyword (158)
• DeviceScan: from MIT Reality Mining• Time: the day scanning happened (1/1/2004-
5/5/2005, 294)• Event: blue tooth device scanning person (114, 046)• Entities: Device (103) & Person (97)• Attribute: NA
61
T3 on `CIKM’ Data Set Rep. Authors Rep. Keywords
James. P. CallanW. Bruce Croft
James AllanPhilip S. Yu
George KarypisCharles Clarke
WebCluster
ClassificationXML
LanguageStream
Rep. Authors Rep. KeywordsElke Rundensteiner
Daniel MirankerAndreas Henrich
Il-Yeol SongScott B Huffman
Robert J. Hall
KnowledgeSystem
UnstructuredRule
Object-orientedDeductive 62
MT3 on `DeviceScan’ Data Set
Aggregate by Month
Apr. 2004 is anomaly
Aggregate by Day
Work day
Semester Break & Holiday
63
Roadmap• Introduction• Completed Work
–Querying–Mining
• Proposed Work–P1: Community detection–P2: Mining Space–P3: Diffusion Wavelets
64
Thesis Overview
65
CePS, G-Ray, ProSIN (KDD06, KDD07 a, ICDM08)Q1
FastProx (ICDM06, KAIS07, KDD07 b, ICDM08)Q3
pTrack/cTrack (SDM08, SAM08)Q2
DAP(KDD07 b)Q2
FastProx(SDM08, SAM08)Q3P3
Colibri-D(KDD08 b)
M1
T3/MT3 (CIKM08)
M2
P1M3P1M3
Colibri-S(KDD08 b)M1 P3
P3
Completed Proposed
Questions That We Ask
P2M2 P3
Detecting Communities
• Observations: two seemingly opposite efforts in community detection– E1: parameter-free (no user intervention)– E2: cluster w/ constraints (listen to users)
• Challenge: How to fill the gap?• Idea: MDL-based method, encoding the
constraints in descriptions.
66
P1
Mining Space
67
P2
Diffusion Wavelets
68
P3
Time Line• Dec. ‘08: Thesis Proposal• Jan. – Feb., ‘09:
– Research on Community Detection
• Mar. – Apr. ‘09: – Research on Mining Space
• May – Jul. ‘09: – Research on Diffusion Wavelets
• Aug. ‘09: Thesis Write-up• Sep. ‘09: Defense
69
P3
P1
P2
Selected References• H. Tong & C. Faloutsos. (2006) Center-piece subgraphs: problem definition and fast
solutions. In KDD, 404-413, 2006.• H. Tong, C. Faloutsos, & J.Y. Pan. (2006) Fast Random Walk with Restart and Its
Applications. In ICDM, 613-622, 2006. (b.p. award)• H. Tong, Y. Koren, & C. Faloutsos. (2007) Fast direction-aware proximity for graph
mining. In KDD, 747-756, 2007.• H. Tong, B. Gallagher, C. Faloutsos, & T. Eliassi-Rad. (2007) Fast best-effort pattern
matching in large attributed graphs. In KDD, 737-746, 2007.• H. Tong, S. Papadimitriou, P.S. Yu & C. Faloutsos. (2008) Proximity Tracking on Time-
Evolving Bipartite Graphs. in SDM 2008. (b.p. award)• H. Tong, S. Papadimitriou, J. Sun, P.S. Yu & C. Faloutsos. (2008) Fast Mining of Static
and Dynamic Graphs. KDD 2008• H. Tong, Y. Sakurai, T. Eliassi-Rad, and C. Faloutsos. Fast Mining of Complex Time-
Stamped Events CIKM 08• H. Tong, H. Qu, and H. Jamjoom. Measuring Proximity on Graphs with Side Information.
ICDM 2008
70
My other work during Ph.D study• GhostEdge (w/ Brian, Christos and Tina, in KDD 08)
– Classification in Sparsely Labeled Network• GMine (w/ Junio, Agma, Christos and Jure, in VLDB 06)
– Interactive Graph Visualization and Mining• Graphite (w/ Polo, Christos, Jason, Brian and Tina, in ICDM 08)
– Visual Query System for Attributed Graphs • TANGENT (w/ Kensuke and Christos)
– ``surprise-me’’ recommendation • PaCK (w/ Jingrui, Spiros, Tina, Jaime and Christos)
– Community detection for heterogonous graphs
71
Acknowledgements
• Christos Faloutsos, Jia-Yu Pan, Yehuda Koren, Spiros Papadimitriou, Philip S. Yu, Jimeng Sun, Huiming Qu, Hani Jamjoom, Tina Eliassi-Rad, Brian Gallagher, Yasushi Sakurai,
• Kensuke Oonuma, Duen Horng (Polo) Chau, Jason I. Hong, Jingrui He, Jaime Carbonell, José Fernando Rodrigues Jr., Jure Leskovec Agma J. M. Traina,
• Charalampos (Babis) Tsourakakis, Meng Su72
(the old way)
CePSProSINGray
DAP
pTrackcTrack
BLin
BBLin
FastUpdateFastDAP
Fast-ProSIN
Colibri
P1
P3
GhostEdge
Graphite
Pack
TANGENT
GMine
T3/MT3P2
MiningQ1
Q2
Q3
M2M3
M1
A Graph Miner’s Way: My Collaboration Graph (During Ph.D Study)
Legends:Green: QueryingBlue: MiningPurple: Others : Completed : Proposed
Q & A
Thank you!
74
